LAN based Dropbox-like alternative ?

Look into SFTP.

SFTP (Secure File Transfer Protocol) is a program that allows files to be exchanged over the Internet in a safe and confidential manner.

Unlike standard FTP, SFTP uses SSH (secure shell) technology, which encrypts both commands and data, preventing passwords and sensitive information from being transmitted in the clear over the network.

I know I'm late to the party, but since I arrived here via google, I'm sure there are others that are seeking similar information to what the original poster was asking.

Fletch711, why not set up a VPN?

http://www.buchatech.com/2010/06/how-to-setup-vpn-acces...

Skippy27, please don't spread disinformation. Not only did you not answer the mans question, you also are answering questions you are obviously not knowledgeable about. Even a quick Wikipedia read would have set you straight.

http://en.wikipedia.org/wiki/SSH_File_Transfer_Protocol

You are only half correct, yes SFTP is a secure transfer protocol. However, it is not a program, it is, as the name states, a TRANSFER PROTOCOL.

Certain FTP programs or such as Filezilla and web development applications such as Adobe Dreamweaver will let you conect to a server using a secure shell connection which will encrypt the data coming and going between your client computer and the server.